Kirchhoff's laws (KCL & KVL)
The two conservation laws all circuit analysis stands on. KCL: current into a node equals current out (charge doesn't pile up). KVL: voltages around any closed loop sum to zero (potential is single-valued).
In practice
Node-voltage analysis is just KCL written systematically — it's what circuit solvers (including this site's engine) do under the hood: one KCL equation per node, solve the system, every voltage and current falls out.